(CNN) - If Republicans suffer losses in next year's mid-term elections because of the recent partial government shutdown, Sen. Ted Cruz said Senate Republicans–not Democrats–will be responsible.

"The single-most damaging thing that has happened to Republicans for 2014 is all of the Senate Republicans coming out, attacking the House Republicans, attacking those pushing the effort to defund Obamacare and lining themselves up opposite of the American people," Cruz told CNN Chief Congressional Correspondent Dana Bash in an interview in San Antonio.Follow @politicaltickerFollow @KilloughCNN

His comments, which aired Monday on "New Day," come as a new CNN/ORC International survey indicates that more than half of the country is displeased with Republicans holding majority power in the House.

According to the poll, 54% say it's a bad thing that the GOP controls the House, up 11 points from last December, soon after the 2012 elections when the Republicans kept control of the chamber. Only 38% say it's a good thing the GOP controls the House, a 13-point dive from the end of last year.
Cruz to CNN: ‘I don’t work for the party bosses in Washington’

This is the first time since Republicans won back the House in the 2010 elections that a majority of people say GOP control of the chamber is bad for the country.

Cruz helped lead the conservative Republican strategy to attach anti-Obamacare provisions to must-pass spending legislation this fall. With the support of the White House, the Democratic-controlled Senate refused to take up anything that tried to dismantle the president's signature health care law.

Many Senate Republicans rebuked the effort led by Cruz, a first-year senator who was elected in 2012, and they privately and publicly discouraged the senator from pursuing the tactic.

"It was a fool's errand to start with. It was never going to succeed," Sen. John McCain said Sunday on CNN's "State of the Union."

McCain didn't single out Cruz but blamed "the whole effort" instead.

"Keep up the fight against Obamacare. But don't shut down the government and have so much collateral damage," the Arizona Republican added.

Some argue Cruz's strategy was taken in part to raise money for conservative groups that back primary challengers. One group, the Senate Conservatives Fund, which supported Cruz last year, raised $2.1 million in September–a large amount for a nonelection year.

Asked if his effort was a money-making enterprise, Cruz said: "Not remotely."

The Texas Republican said he's "hopeful" Senate Republicans will change.

"I am hopeful there will be some time, some reflection, and that Senate Republicans will come back. Come back to the principles they believe and they campaigned on. I'm hopeful we'll actually put action behind the campaign promises," he said.

In the Senate, Democrats hold 55 seats, including two independents who caucus with the Democrats, while Republicans hold 45. Democrats are defending 21 of the 35 seats up for grabs next year, with Republican defending 14.